# An economic production model with imperfect quality components and probabilistic lead times

Abdul-Nasser El-Kassar (Information Technology and Operations Management, Lebanese American University, Beirut, Lebanon)
Alessio Ishizaka (NEOMA Business School, Mont-Saint-Aignan, France)
Yama Temouri (Khalifa University, Abu Dhabi, UAE) (Aston University, Birmingham, UK)
Abdullah Al Sagheer (Advisor for the Minster of Public Works, Minister's Office Department, Kuwait)
Daicy Vaz (Humanities and Social Sciences, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates)

ISSN: 0957-4093

Article publication date: 3 November 2020

Issue publication date: 29 April 2021

325

## Abstract

### Purpose

This study investigates a production process that requires N kinds of components for the production of a finished product. The producer orders the various kinds of components from different suppliers and receives the orders in lots at the beginning of each production cycle. Similar to situations often encountered in real life, the lead times are random variables with known probability distributions so that a production cycle starts whenever all N kinds of components become available. Each of the lots received at the start of a production run contains both perfect and imperfect quality components. Once all N kinds of components become available, the producer initiates a screening process to detect the imperfect components. The production of the finished product uses only perfect quality components. The imperfect components are removed from inventory whenever the screening process is completed. The percentage of components of perfect quality present in each lot is a random variable with a known probability distribution.

### Design/methodology/approach

This production process is described and modeled mathematically and the optimal production/ordering policy is derived based on the mathematical model.

### Findings

The formulated mathematical model resulted in the determination of the optimal policy consisting of the optimal number of finished items ordered to be produce during each production run, the number of components ordered from each supplier, and the reorder point. The derived closed form expression for the optimal lot size depends on the minimum of the number of perfect quality components in a lot, whereas the reorder point is determined based on the maximum lead time.

### Practical implications

The modeling approach and results of this study provide practical implications that may be beneficial to both production and supply chain managers as well as researchers.

### Originality/value

This modeling approach that incorporates decision-making related to the logistics of acquiring the components and accounts for the probabilistic nature of the lead times and quality of components addresses a gap in the logistics/production literature.

## Acknowledgements

This paper forms part of a special section “Decision Making in Logistics Management in the Era of Disruptive Technologies”, guest edited by Vijay Pereira, Gopalakrishnan Narayanamurthy, Alessio Ishizaka and Noura Yassine.

## Citation

El-Kassar, A.-N., Ishizaka, A., Temouri, Y., Al Sagheer, A. and Vaz, D. (2021), "An economic production model with imperfect quality components and probabilistic lead times", The International Journal of Logistics Management, Vol. 32 No. 2, pp. 320-336. https://doi.org/10.1108/IJLM-02-2020-0074

## Publisher

:

Emerald Publishing Limited